In the triangle ABC, the angle c is 90 BC = 6 sine a = 3 / √34 find AC

Let us determine the length of the hypotenuse AB through the leg BC and the opposite angle.

AB = BC / SinBAC = 6 / (3 / √34) = 2 * √34 cm.

By the Pythagoras theorem, we determine the length of the leg AC.

AC ^ 2 = AB ^ 2 – BC ^ 2 = 136 – 36 = 100.

AC = 10 cm.

Second way.

Let’s define the cotangent of the angle BAC through the sine of this angle.

Ctg2BAC = (1 / Sin2BAC) – 1 = (1 / (9/34) – 1 = (34/9) – 1 = 25/9.

CtgBAC = 5/3.

Then CtgBAC = AC / BC.

AC = BC * CtgBAC = 6 * 5/3 = 10 cm.

Answer: The length of the AC leg is 10 cm.